Diffusion-weighted imaging (DWI) is a magnetic resonance imaging (MRI) technique for mapping the diffusion of molecules, such as water, within biological tissue. Diffusion tensor imaging (DTI) is subfield of DWI, which has been used extensively to map white matter tractography in the brain.
DTI scan data is sometimes presented as a diffusion ellipsoid map. Each ellipsoid is associated with a respective voxel in a slice of the imaged tissue, and is accordingly centered about map coordinates corresponding to the centerpoint of the respective voxel in the slice (such that all the ellipsoids, which are three-dimensional, are centered about respective map coordinates on a single flat plane—the map plane). The dimensions and orientation of each ellipsoid are determined by the diffusion tensor associated with the respective voxel (see, for example, Basser et al., Biophysical Journal, 66, p. 259, 1994). More specifically, the length and orientation of each of the three principal axes of an ellipsoid are determined by a respective eigenvalue-eigenvector pair of the associated diffusion tensor. The eigenvalues λ2, and λ3 (usually defined such that λ1≥λ2≥λ3) equal the diffusion coefficients along three orthogonal directions defined by the corresponding eigenvectors v1, v2, and v3, respectively.
Typically, in DTI brain imaging, each ellipsoid is colored according to the direction (i.e. v1) in which the respective largest principal axis (having a length λ1 or a length proportional to λ1, including, but not limited to, √{square root over (λ1)}) thereof points, as well as including light and shade effects to better visually impart the three-dimensional shape thereof. For example, if the largest principal axis is closest to the x-axis, y-axis, or z-axis (of a laboratory, Cartesian frame of reference), the ellipsoid is colored in either blue, red, or green, respectively. In some ellipsoid maps, the ellipsoids may be colored as a combination of blue, red, and green, weighted according to the proximity of the largest principal axis to each of the respective axes of the laboratory frame.
The past decade has seen the application of DWI, including DTI, to cancer detection in the breast. Water diffusion in mammary ducts and lobules in the breast is anisotropic, being fast along the length of a duct/lobule and restricted in directions perpendicular to the length of the duct/lobule. Without being bound to any theory or mechanism, the presence of cancer cells in a region of the breast is believed to bring about the blockage/partial blockage and physical deformation of mammary ducts/lobules and the surroundings thereof in the region, with a resultant reduction in the diffusion rate, and the anisotropy of the diffusion, through the mammary ducts/lobules. Accordingly, low λ1 values have been found to be indicative of breast cancer. Alternatively, or in addition, the absolute maximal anisotropy index, defined as λ1-λ3, assumes low values in the presence of breast cancer. See E. Eyal et al., Invest. Radiol. 2012 47(5):284-91; N. Nissan et al., J. Vis. Exp. (94), e52048, 2014; E. Furman-Haran et al., J. Magn. Reson. Imaging, 2016, doi: 10.1002/jmri.25292 [Epub ahead of print]; E. Furman-Haran et al., Europ. J Radiol. 81, S 45-47, 2012; and M. Shapiro Feinberg et al., Europ. J Radiol. S 151-152, 2012. The contents of all the above-cited publications is incorporated herein by reference.
Diffusion ellipsoid maps of the breast were presented in J. R. Teurel et al., J. Magn. Reson. Imaging, 2016 May; 43(5):1111-21, the contents of which are incorporated herein by reference, and in Furman-Haran et al., 2016, ibid. In the former publication, the diffusion ellipsoids were all colored in the same color. In the latter publication, the diffusion ellipsoids were colored according to the orientation of the respective largest principal axis, as elaborated on above for brain imaging.
U.S. Pat. No. 8,526,698 to Degani, the contents of which are incorporated herein by reference, discloses a method, apparatus and computer product for imaging a human breast to map the breast ductal tree. First, a breast is diffusion tensor imaged with high spatial resolution. Then the breast ductal tree is tracked using a protocol for: breast based on echo-planar imaging (EPI) diffusion designed for optimizing diffusion weightings (b values), number of non-collinear directions for tensor calculations, diffusion, echo and repetition times, spatial resolution, signal to noise, scanning time, and a sequence for fat suppression. The diffusion tensor is calculated by a non-linear best fit algorithm and then diagonalized (e.g. using principal component analysis) to obtain three eigenvectors and their corresponding eigenvalues. A vector field map is obtained for tracking of breast ducts of the ductal trees along the direction of the 1st eigenvector v1 and the ductal tree is displayed on a voxel by voxel basis in parametric images using color coding and vector pointing.